Final answer:
The distance between the points (4,2) and (0,-1) is 5 units, and the midpoint is (2, 0.5). Calculations are performed using the distance formula and by averaging coordinates for the midpoint.
Step-by-step explanation:
To find the distance between the points (4,2) and (0,-1), we use the distance formula derived from the Pythagorean theorem:
d = √[(x2 - x1)2 + (y2 - y1)2]
Plugging in our points gives us:
d = √[(0 - 4)2 + (-1 - 2)2] = √[(-4)2 + (-3)2] = √[16 + 9] = √25 = 5
The midpoint between the points is found by averaging the x-coordinates and the y-coordinates separately:
Midpoint (M) = ((x1 + x2)/2, (y1 + y2)/2)
M = ((4 + 0)/2, (2 + -1)/2) = (2, 0.5)